If you can solve this I will give you a million dollars
Since AQ is an angle bisector, angle CAQ is 45 degrees. We are told that angle PAQ is 13 degrees, so angle RAC is 45 + 13 = 58 degrees.
Wait you wont give the person who solves this one million dollars i bet :p
Assuming that P, Q, and R are on BC (in the order B, P, Q, R, C):
Angle(BAC) = 90.
Since AQ is an angle bisector, angle(BAQ) = 45.
Since P is between B and Q and angle(PAQ) = 13, angle(BAP) = angle(BAQ) - angle(PAQ)
---> angle(BAP) = 45 - 13 = 32.
Since AP is an altitude, angle(BPA) = 90.
In triangle(BAP), angle(BAP) = 32 and angle(BPA) = 90 ---> angle(ABP) = 58.
In triangle(BAC), angle(BAC) = 90 and angle(ABP) = 58 ---> angle(ACB) = 32.
Since AR is a median of a right triangle, RA = RB = RC.
Since RA = RC, triangle(ARC) is an isosceles triangle.
Since angle(ACB) = 32, ange(CAR) = 32.